Vladimir Putin still pulls the strings in Russia, with President Dmitry Medvedev a more junior figure who "plays Robin to Putin's Batman", US diplomats have said in frank dispatches from Moscow released by WikiLeaks.

Since Putin stepped down as president in 2008, political analysts have been scrambling to assess whether he – or his handpicked successor, Medvedev – is Russia's real leader. After leaving the Kremlin, Putin immediately became prime minister.

Secret diplomatic cables seen by the Guardian reveal the US emphatically believes Putin to be in charge. They also suggest Putin will decide whether Medvedev serves a second term, whether he will return to the presidency himself or give the job to someone else. In a dispatch sent in February 2010, the US ambassador in Moscow, John Beyrle, dubbed the pairing "Russia's bicephalous ruling format". He made clear that he saw Putin as the more important of the two heads.

"Medvedev and Putin work well together, but Putin holds most, and the best, of the cards in the tandem relationship. His return to the Kremlin is not inevitable, but should things remain stable, Putin remains in a position to choose himself, Medvedev, or another person as Russia's next president."

In a separate cable the Azeri president, Ilham Aliyev, is recorded telling a top US official that he personally witnessed Medvedev taking decisions that then required further approval. Some were stymied at that stage, presumably in the prime minister's office.

"Many high-ranking officials don't recognise [Medvedev] as a leader ... There are signs of a strong confrontation between the teams of the two men, although not yet between Putin and Medvedev personally.'"

Aliyev continued: "We have a saying in Azeri: two heads cannot be boiled in one pot." The writer of the cable explained that this was "crude street slang suggesting that two leaders are spoiling for a fight".

Putin and Medvedev have left pundits guessing as to their intentions before an election in the spring of 2012. Both have indicated they may stand again as president. Putin stepped down after two four-year terms, in accordance with Russia's constitution. This has now been changed, giving the next president a six-year stint.

The cables reveal how the US embassy industriously canvassed views from a range of Moscow experts on Russia's unusual political duopoly. In a November 2009 cable, the deputy ambassador, Eric Rubin, lumped the experts' opinions into three "very divergent camps".

The first group, he reported, believed Medvedev was ascending and "slowly accruing power". The second, more sceptical group "argues that Medvedev continues to play Robin to Putin's Batman". And the third saw "no essential difference" between the two.

In reality, however, nobody knew what was going on in the Russian corridors of power, the cable admited. "All are hindered by the impenetrable nature of Kremlin politics and the fertile field of speculation and rumour that the information vacuum creates," Rubin said.

The US ambassador illustrated Putin's supremacy by retelling a joke doing the rounds in Moscow. "Medvedev sits in the driver's seat of a new car, examines the inside, the instrument panel, and the pedals. He looks around, but the steering wheel is missing. He turns to Putin and asks: 'Vladimir Vladimirovich, where is the steering wheel?' Putin pulls a remote control out of his pocket and says: 'I'll be the one doing the driving.'"

US officials advised that looking for splits in the Putin-Medvedev tandem was a waste of time. They also said gullible Europeans and Americans who believed Medvedev was more enlightened than Putin were probably fooling themselves.

"A search for evidence of dissonance between the two leaders is either the forlorn hope of western-leaning liberals ... or a legacy of 'Kremlinology' that presupposes inter-leadership conflict as the sine qua non of Russian politics," Rubin said.

Two years after Putin left the Kremlin he was a "mythic figure" for many Russians and enjoyed high popularity ratings, the cables said. Putin engaged with "meat and potatoes" issues and was easier to understand than the sometimes waffle-prone Medvedev, they suggested.

The cables noted the weak nature of Medvedev's electoral base, estimating he enjoyed the support of 20% of "urbanites" – voters in Moscow and St Petersburg. Putin, by contrast, had the backing of 80% of "ordinary Russians".

During a question and answer session on live TV last December, Putin "highlighted his role as Russia's dominant political figure", the cables said. He fielded questions on a wide range of questions and demonstrated a populist flair that had so far eluded the more cerebral, ex-lawyer and Deep Purple fan Medvedev. But it isn't just the Americans wondering who is in charge of the world's largest country and its formidable nuclear arsenal. Russian government ministers have also expressed confusion.

Abiyev told the Americans that "after the second bottle of vodka" the Russians opened up. The cable went on: "In an interesting side note, Abiyev quoted Serdyukov as saying: 'Do you follow the orders of your president? ... Well I follow the orders of two presidents."